The nucleus of an atom of ${{}_{92}\mathrm{Y}}^{235}$, initially at rest, decays by emitting an $\alpha$ -particle as per the equation :
${}^{235}\mathrm{Y}_{92}\to {}^{231}\mathrm{X}_{90}+{}^4\mathrm{He}_2+$ energy.
It is given that the binding energies per nucleon of the parent and the daughter nuclei are $7.8\mathrm{MeV}$ and $7.835\mathrm{MeV}$ respectively and that of $\alpha$ -particle is $7.07\mathrm{MeV}/$ nucleon. Assuming the daughter nucleus to be formed in the excited state and neglecting its share in the energy of the reaction, calculate the speed of the emitted $\alpha$ -particle. Take mass of $\alpha$ -particle to be $6.68\times {10}^{-27} \mathrm{kg}$.